The research in David Nelson's group focuses on collective effects in the physics and chemistry of condensed matter, as well as on physical biology. He has long been interested in the interplay between fluctuations, geometry and statistical mechanics in both classical and quantum systems. In collaboration with his colleague, Bertrand I. Halperin, he is responsible for a theory of dislocation-mediated melting in two dimensions. The prediction of Halperin and Nelson of a fourth "hexatic" phase of matter, interposed between the usual solid and liquid phases, has now been confirmed in experiments on thin films and bulk liquid crystals, in both planar and spherical geometries.
Nelson's physics and physical chemistry research includes a theory of the structure and statistical mechanics of metallic glasses and investigations of "tethered surfaces,” which are two-dimensional generalizations of linear polymer chains. These fishnet-like structures exhibit a remarkable low temperature flat phase upon cooling. This flat phase has been observed both in the spectrin skeletron of red blood cells and, more recently, in free-standing atomically thin graphene cantilevers. Nelson has also studied the flux line entanglement in high temperature superconductors. At high magnetic fields, thermal fluctuations cause regular arrays of flux lines to melt into a tangled spaghetti state. The physics of this melted flux liquid has important implications for many of the proposed applications of these new materials. His current physics interests include vortex physics, the statistical mechanics of sheet polymers with holes, slits and puckers, topological defects on frozen topographies, the interplay between quantum degrees of freedom, and flexural phonons in free-standing atomically thin materials like graphene and MoS2.
Approximately half of Nelson’s recent research has focused on problems that bridge the gap between the physical and biological sciences. His interests in physical biology include the shapes of viruses, dislocation dynamics in bacterial cell walls, range expansions and genetic demixing in microorganisms, and spatial localization in asymmetric sparse neural networks. Together with David Lubensky, Nelson developed a theory of force-induced denaturation of double-stranded DNA. Sequence heterogeneity dominates the dynamics of the unzipping fork (with possible implications for DNA replication in prokaryotes) over a large range of forces above an unzipping transition. Nelson and colleagues have also studied the shapes of viruses, showing that the icosahedral packing of protein capsomeres of spherical viruses becomes un-stable to faceting for sufficiently large virus size. A parametization of the architecture of virus shells in terms of single dimensionless “von Karman number” shows why small viruses are round while large ones are faceted. His work on spatial population genetics began with a semester during which he worked in the biology laboratory of Sharad Ramanathan, where he and Oskar Hallatschek began exploring range expansions of genetically diverse microorganisms on a Petri dish. These investigations were later adapted, with help from his biology colleague, Andrew Murray, to explore the effects of selective advantages, mutualism, obstacles and antagonism on microorganisms that compete in space, including those growing at liquid/air interfaces. With Roberto Benzi and Federico Toschi, he has a long-standing interest in combining spatial population genetics with fluid flow, at both high and low Reynolds numbers.
